Bill de Blasio and Bill Bratton during a press conference at Gracie Mansion Sunday November 2nd. Robert Kalfus

Mayor de Blasio and Police Commissioner Bill Bratton held a press conference Sunday, bashing The Post for its coverage of their relations. First Lady Chirlane McCray even posted a statement on her Web site denying our reporting.

The Post stands by its reports, but let’s face it: This is no way to run a police department. Start with the fact that Bratton is the NYPD’s commissioner, at least nominally, and a commish is generally given latitude to run his department as he sees fit, including on staffing matters. That’s because he would bear much of the blame should crime spike.

But when Philip Banks, who is black, quit Friday rather than be promoted by Bratton to the NYPD’s No. 2 spot — reportedly because Banks believed the post lacked power — he became the second top-ranking minority to quit, following Rafael Piñeiro, who left Friday. And all hell broke loose.

Fact is, Bratton was publicly humiliated, including by de Blasio. The mayor was said to have been furious that Bratton allowed Banks to quit, and he let Bratton know it. On Sunday, The Post reported the mayor’s wife railed at de Blasio for having ignored her warnings about Bratton.

Meanwhile, the usual suspects pounced. The Rev. Al Sharpton demanded the NYPD place “blacks and Latinos in senior positions, and de Blasio reportedly had to make nice with the Rev. City Comptroller Scott Stringer and Public Advocate Letitia James called for diversity in “police leadership.”

No police commissioner can operate this way, and, sure enough, Bratton is now vowing Banks’ replacement will be someone with whom minorities will be “very pleased.”

This is life on Planet de Blasio. A commissioner is normally expected to make staffing decisions based on who he thinks is best for the job. But de Blasio has put Bratton in a bind, given the mayor’s anti-cop record and his tacit orders that racial pandering — and pleasing Sharpton — take priority over crime-fighting.

That leaves the commish three choices: Do de Blasio’s bidding and risk a crime surge (and a blow to his reputation). Ignore his boss, do the right thing for the city — and risk being fired. Or simply quit.

And it leaves New Yorkers who care about their safety without any good options.